Eric traveled to three cities on a single highway. The distance from his original location to the first city was 100 miles more than 1/3 the distance from the first city to the second city. The distance from the second city to the third city was 10 miles less than 5/4 the distance from the first city to the second city. If the distance from his original location to the first city and the distance from the second city to the third city were the same, what was the total distance Eric traveled?

Question

Jonathan Lamb

Mathematics

9 October, 11:03

Eric traveled to three cities on a single highway. The distance from his original location to the first city was 100 miles more than 1/3 the distance from the first city to the second city. The distance from the second city to the third city was 10 miles less than 5/4 the distance from the first city to the second city. If the distance from his original location to the first city and the distance from the second city to the third city were the same, what was the total distance Eric traveled?

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Answers (1)

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Baylee Eaton · Answer 1

Let the distance between the origin and the 1st city = D = The distance between 2nd and 3rd city.

Let the distance between 1st and 2nd city = d, then:

The distance between origin and 1st city = 1/3d + 100, and

The distance between 2nd and 3rd city = 5/4d - 10. But we have:

1/3d + 100 = D ... (1), and

5/4d - 10 = D ... (2), but

1/3d + 100 = 5/4d - 10, solve for d

d = 120 miles - distance between 1st and 2nd city.

1/3 x 120 + 100 = 140 miles - distance between origin and 1st city.

5/4 x 120 - 10 = 140 miles - distance between 2nd and 3rd city.

140 + 120 + 140 = 400 miles - total distance travelled.